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Hadwiger's conjecture, first formulated in 1943, is a vast generalization of the four-color theorem, and remains one of the central open problems in

The tree-independence number of a graph is the analogue of treewidth where, instead of minimising the size of bags, we minimise the size of a stable

The celebrated Linear Arboricity Conjecture of Akiyama, Exoo, and Harary from 1980 asserts that the edges of every graph with maximum degree Δ can be

We study biased Maker-Breaker games on a graph system {G1,…,Gs}, in which Maker's goal is to claim certain rainbow structures, i.e., specified

A triangulation of a surface is k-irreducible if every edge belongs to a non-contractible curve of length k and there are no shorter non-contractible

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We will look at an analogue theorem of the classical Erdős-Pósa Theorem. We prove a $GF(q)$-representable matroid analogue of Robertson and Seymour's

A landmark result of Alon and Shapira characterises testable graph properties by showing that every such property can be described via the Szemerédi

In 1943, Hadwiger conjectured that every k-chromatic graph has a K_k-minor. While the cases k = 5 and k = 6 have been shown to be equivalent to the

A temporal graph G is a sequence of graphs G1, G2, ... , Gt on the same vertex set. In this talk, we are interested in the analogue of the Travelling